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If someone cancels a $10 fee on your account, your balance doesn't go down—it actually goes up.
Taking away a negative amount has the exact same effect as handing you cash.

The Additive Inverse

An additive inverse is just the opposite of a number—the exact value you add to it to land at zero.
For example, the opposite of 66 is −6-6, and the opposite of −35-\frac{3}{5} is 35\frac{3}{5}.
Back in 628 CE, the Indian mathematician Brahmagupta wrote the first formal rules for negative numbers, observing that subtracting a debt is the same as gaining a fortune.
This leads to the Fundamental Subtraction Principle: subtraction is formally defined across all number systems as the addition of the additive inverse, written as p−q=p+(−q)p - q = p + (-q) for any rational numbers pp and qq.
This rule also explains what happens when subtracting a negative rational number.
Because the additive inverse of a negative number is positive (−(−q)=q-(-q) = q), subtracting a negative simplifies to adding a positive: p−(−q)=p+(−(−q))=p+qp - (-q) = p + (-(-q)) = p + q.

Distance Between Rational Numbers

The geometric distance between rational numbers pp and qq on a number line is given by ∣p−q∣|p - q|, which equals ∣p+(−q)∣|p + (-q)| and ∣q−p∣|q - p|.